Respuesta :

Answer:

The area of the figure is 3.6257188 cm²

The perimeter of the shape is 7.0685835 cm

Step-by-step explanation:

Let us find the area of the shape at first

∵ The shape formed from 3 semicircles and an equilateral triangle

Its area = 3 (area of a semicircle) + area of an equilateral Δ

∵ Area of the semicircle = [tex]\frac{1}{2}[/tex] π r²

∵ The diameter of the semicircle = 1.5 cm

∵ The radius = [tex]\frac{1}{2}[/tex] the diameter

r = [tex]\frac{1}{2}[/tex] × 1.5 = 0.75 cm

∴ The area of a semicircle = [tex]\frac{1}{2}[/tex] π (0.75)²

The area of a semicircle = 0.28125π cm²

→ Find the area of the Δ

∵ Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

∵ The base of the triangle = 1.5 cm

∵ The height of the triangle = 1.3 cm

∴ Area of the triangle =  [tex]\frac{1}{2}[/tex] × 1.5 × 1.3

Area of the triangle = 0.975 cm²

→ Now find the area of the shape

Its area = 3(0.28125π) + 0.975

∴ Its area = 3.6257188 cm²

The area of the figure is 3.6257188 cm²

Now let us find the perimeter of the figure

∵ The perimeter of a figure is the length of the outline sides

The perimeter of the figure = the length of the 3 half circumferences

∵ The length of half the circumference = [tex]\frac{1}{2}[/tex] (2 π r) = π r

∵ r = 0.75 cm

∴ The length of half the circumference = 0.75 π

→ Find the perimeter of the shape

∵ The perimeter of the shape = 3 × 0.75 π

∴ The perimeter of the shape = 7.0685835 cm

The perimeter of the shape is 7.0685835 cm

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